I need suggestions on how to name this operator!
In an upcoming paper, we take a matrix/a vector space endomorphism π΄βEnd(π), together with a subspace of End(π) closed under commutators with some orthonormal basis (πα΅’), and create the mapping
End(π)βEnd(π), π΄β¦πα΅’π΄πα΅’.
(More generally, we can map π΄β¦Ο(πα΅’)π΄Ο(πα΅’) where Ο: π€βπ€π©(π) is any Lie algebra representation and (πα΅’) is an ONB of π€. This map is then related to quadratic Casimir operators of π€.)
Since the endomorphism π΄ gets 'sandwiched' between the πα΅’, we have semi-creatively taken to call this mapping π ππππ€ππh ππππππ‘ππ. Can anyone think of a better name? Or has anyone seen this thing in action before?
Paul Schwahn
npub1zzβ¦59mhx
2024-11-13 17:31:38 UTC
Author Public Key
npub1zz2mah7y6j4nld7dwedl7eh0yph4swkkv88spuvh0urq32xgz3ws459mhxSeen on
wss://relay.momostr.pinkPublished at
2024-11-13 17:31:38 UTCEvent JSON
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"content": "I need suggestions on how to name this operator!\n\nIn an upcoming paper, we take a matrix/a vector space endomorphism π΄βEnd(π), together with a subspace of End(π) closed under commutators with some orthonormal basis (πα΅’), and create the mapping\n\nEnd(π)βEnd(π), π΄β¦πα΅’π΄πα΅’.\n\n(More generally, we can map π΄β¦Ο(πα΅’)π΄Ο(πα΅’) where Ο: π€βπ€π©(π) is any Lie algebra representation and (πα΅’) is an ONB of π€. This map is then related to quadratic Casimir operators of π€.)\n\nSince the endomorphism π΄ gets 'sandwiched' between the πα΅’, we have semi-creatively taken to call this mapping π ππππ€ππh ππππππ‘ππ. Can anyone think of a better name? Or has anyone seen this thing in action before?",
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